Poisson type conformastat spherically symmetric anisotropic fluid spacetimes

TL;DR

This paper develops new models of relativistic anisotropic fluid spacetimes based on Newtonian solutions, constructing thick spherical shells and galaxy-like structures, and analyzes test particle motion within these models.

Contribution

It introduces a method to generate relativistic anisotropic fluid spacetimes from Newtonian potential solutions, including models of galaxies and shells, with positive stresses and energy conditions satisfied.

Findings

Constructed new relativistic anisotropic models of spherical shells and galaxy structures.

Analyzed stable circular orbits of test particles in these spacetimes.

Ensured all energy conditions and positive principal stresses are satisfied.

Abstract

We construct conformastat spherically symmetric spacetimes representing anisotropic fluid matter distributions from given solutions of the Poisson's equation of Newtonian gravity and its corresponding circular speed profile. As simple examples, we present three families of spherically symmetric spacetimes which we apply in constructing new models of relativistic anisotropic thick spherical shells, and of relativistic galaxy models composite by a central spherical bulge, the thick disk and the dark matter halo, writing in this case the metric in cylindrical coordinates. Moreover, the geodesic motion of test particles in stable circular orbits around such structures is studied. We build anisotropic fluid sources for these spacetimes which satisfy all the energy conditions and the principal stresses are positive quantities (pressure).